Elements of Geometry upon the Inductive Method; to Which Is Added an Introduction to Descriptive Geometry
Format: Paperback
ISBN13: 9781150213342
Paperback|9781150213342
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated.1829 Excerpt: ...-r.ach, the angles are respectively equal to the angles of the field, and their dimensions also proportional to the corresponding dimensions of the field. Hence we have the general truth--Two similar rectilinear figures have the angles of the one equal to the angles of the other, each to each, and all homologous lines proportional. 93. Remark. If diagonals were drawn through corresponding vertices in the two polygons; being homologous dimensions, they would be proportional; and being proportional, the triangles into which these diagonals divided the two figures would be similar respectively. We say therefore, that--Similar polygons are composed of the same number of similar triangles, similarly placed. 94. If the several sides of a polygon were represented by A, B, C, D, E, and the corresponding sides of a similar A B polygon, by a, b, c, d, e; we should have (92)--= j= C D E--=-j-=--; from which we obtain (84), c a e A + B + C +D + E_A a--b--c--d--e a' that is--In similar polygons, the perimeters are propor-tional to their homologous sides. 95. In the base of the triangle ABC (fig. 45), take A c j-ig. 45, of any convenient magnitude, and draw c b parallel to CB; we shall have the triangle A c b, equiangular with ACB (24), and therefore similar to it (91). Hence--If a triangle is cut by a straight line parallel to one of the sides, the small triangle cut off is similar to the whole. These similar triangles give the proportion AC AB, . /Ql, AC--Ac AB--Ab AT=A6; therefore (81), ----zz: _-; that is, ---=-r-r; and the line c b divides the two sides Ac Ao AB and AC, proportionally. Thus we have the general rule, --A straight line drawn through any triangle parallel to one of the sides, divides the other two sides proportionally. The converse of these two proposition
| ISBN-13 | 9781150213342 |
|---|---|
| ISBN-10 | 1150213345 |
| Weight | 0.47 Pounds |
| Dimensions | 9.00 x 6.00 x 0.32 In |
| List Price | $19.99 |
| Format | Paperback |
|---|---|
| Pages | 138 pages |
| Publisher | |
| Published On | 2009-12-01 |
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